"Down these mean streets a man must go who is not himself mean."
In Support Your Local Sheriff! Jason McCullough (played by James Garner) is the mysterious stranger who comes to town. He is an excellent shot and a very quick draw and has the sort of confidence in dealing with violence that comes from long experience. It is clear, moreover, that he lives by a code of only taking on challenges that are comfortably within his skill set, and only when absolutely necessary.
Indeed, although it's unclear whether he actually ever meant it, he is not even initially interested in appearing courageous in any conventional sense. If the job becomes impossible, he does not have any scruples about leaving it behind. It's only when he tells the woman with whom he is increasingly smitten that he intends to leave town that he realizes how cowardly that sounds. And then he finds a way of meeting the gang of thugs that is descending on his town in a way that will give him a victory without having to cause a "massacre".
In the movie he never once meets an equal in anything he does. The closest he comes to an actual challenge is one in which he is seriously outnumbered. It should be noted, however, that he survives one encounter by luck. Or, rather, he is saved by someone he could not, as he himself points out, reasonably have counted on to save him. That, too, however seems to be something he has experience with. He has a kind of "grace". And he knows it.
We like McCullough for a simple reason, I think. His competence greatly exceeds his interest in succeeding. He doesn't want a "reputation" (because that "is likely to get a man killed".) He moves among men who are sometimes well-meaning, sometimes entirely malevolent, but generally ambitious and inept. In a word, McCullough is "cool". His competence is not stretched to the limit by his striving. He is working from the center of his strength and this keeps his nature good.
And he succeeds. He rounds up the bad guys. He gets the girl and makes her his wife. (She's even the richest girl around for miles!) And as we are told in the epilogue, he goes on to become governor of the state. He's a man worthy of our support.